Unit 18 Section 1 : Presentation of Quantitative Data

In this section we will look at how vertical line diagrams can be used to display discrete quantitative data.
Discrete quantitative data is data which can only take specific numerical values (e.g. Marks out of ten in a test).

Example
The marks below were scored by the children in a class on their maths test. All the marks are out of ten.
To organise these data, a tally chart has been produced. We first saw tally charts in book 7A.

Raw Data
Tally Chart
Another way to represent these data is by drawing a vertical line diagram on squared paper.
The vertical line diagram for this data is shown on the right.

The height of each bar represents the frequency.
The frequency is the number of times each item occurs.

For example:
The score 6 occurred 5 times, so the "6" line is 5 units high.
Only 1 person scored 10, so the "10" line is only 1 unit high.
Nobody scored 1, so there is no "1" line on the diagram.

Practice Questions
Work out the answer to these questions using the chart above, then click Click on this button below to see the correct answer to see whether you are correct.
(a) What is the most common mark?
(b) What is the highest mark?
(c) What is the lowest mark?
(d) What is the difference between the highest and lowest marks?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

When you want to draw lines on a vertical line diagram in the questions below, click where you want the top of the line to be. If you want to change the height of the line, click at a different height on the same line. If you want to remove a line, click the square at the top of the line. Practise this on the vertical line diagram in Question 1.
You may find it helpful to have some paper to do tally charts for some of these questions.

Question 1
A teacher gives the children in her class a test, and lists their scores in the table below:
(a) Fill in the vertical line diagram on the right, using this data, then click on the button to see if you are correct.

(b) What is the most common mark?

(c) How many children are there in the class?

Question 2
The staff in a shoe shop keep a record of the sizes of all the shoes they sell in one day. Their results are listed below.

(a) Fill in the vertical line diagram on the right using this data, then click the button below to see if you are correct. You may find it helpful to make up a tally chart on paper before you mark in the vertical lines.

(b) How many pairs of shoes were sold in total on this day?

(c) What is the most popular size of shoe?

Question 3
The vertical line diagram below is based on data collected by a class about the number of children in their families:
(a) What is the most common number of children in a family?

(b) How many children are there in the class?

Question 4
A gardener keeps a record of the number of tomatoes he picks from the plants in his greenhouse during August.
The number of tomatoes picked each day is listed below:

(a) Fill in the vertical line diagram, using this data, then click on the button to see if you are correct.

(b) What is the largest number picked on one day?
tomatoes

(c) What is the smallest number picked on one day?
tomatoes

(d) On some days, less than 7 tomatoes were picked.
On how many days did this happen?
days

Question 5
A sample of children were asked how many pets they had, and their responses are listed below:
(a) Fill in the vertical line diagram, then click the button to see if you are correct.

(b) How many children were asked about their pets?

(c) How many pets are included in the data?

(d) "There are more children who own pets than children who do not own pets." Is this true or false?

Question 6
A rail company keeps a record of how many trains are late each day.

The data for January and February are below:
January Data
February Data

(a) Fill in the two vertical line diagrams below, then click the button under each one to see if you are correct.
(b) Which month had the day with the most late trains?
(c) Which month had the most days with no late trains?

Question 7
Graham is using his calculator to generate random numbers.
The calculator will produce one of the ten numbers from 0 to 9 at random.
Graham wants to investigate if the numbers are really random.
He uses his calculator to produce 40 random numbers.
(a) How many times would you expect each number to appear?

Below are the 40 numbers the calculator produced:

(b) Fill in the vertical line diagram using this data, then click the button to see if you are correct.
(c) Would you say the numbers generated are evenly random?


You have now completed Unit 18 Section 1
Your overall score for this section is
Correct Answers
You answered questions correctly out of the questions in this section.
Incorrect Answers
There were questions where you used the Tell Me button.
There were questions with wrong answers.
There were questions you didn't attempt.
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Produced by A.J.Reynolds January 2001